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OBJECTIVE FUNCTION HELP!!!











































Consider the objective function z=5x+8y subject to the following constraints:
x+y greater than/equal to 2
2x+3y less than/equal to 12
3x+2y less than/equal to 12
x greater than/equal to 0
y greater than/equal to 0

Find the feasible region and list the corner points.
Corner points:
If there is more than one corner point, type the points separated by a comma (i.e. (1,2),(3,4)).

Find the maximum and minimum values of z.
Maximum value of z is: when x= and y=
Minimum value of z is: when x= and y=

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Apr 17, 2011
OBJECTIVE FUNCTION HELP!!!
by: Staff


The question:

Consider the objective function z=5x+8y subject to the following constraints:

x+y greater than/equal to 2
2x+3y less than/equal to 12
3x+2y less than/equal to 12
x greater than/equal to 0
y greater than/equal to 0

Find the feasible region and list the corner points.

Corner points:

If there is more than one corner point, type the points separated by a comma (i.e. (1,2),(3,4)).

Find the maximum and minimum values of z.

Maximum value of z is: when x= and y=
Minimum value of z is: when x= and y=


The answer:

Consider the objective function z=5x+8y subject to the following constraints:

x+y greater than/equal to 2
2x+3y less than/equal to 12
3x+2y less than/equal to 12
x greater than/equal to 0
y greater than/equal to 0

Find the feasible region and list the corner points.

Maximize

z = 5x + 8y

Subject to:

x + y ≥ 2
2x + 3y ≤ 12
3x + 2y ≤ 12
x ≥ 0
y ≥ 0


When these boundaries are plotted, they form the Bounded Feasible Region (click link to view, use the Backspace key to return to this page):

http://www.solving-math-problems.com/images/objective-function-help-20110417-1a-feasible-region.png


The bounded feasible region (shown as the yellow shaded area) defines a maximum value and a minimum value for the objective function (z = 5x + 8y).


Corner points:

The corner points are shown in the following graph (click link to view, use the Backspace key to return to this page):

http://www.solving-math-problems.com/images/objective-function-help-20110417-1b-corner-points.png


The corner points are:

(2,0), (4,0), (0,2), (0,4), (2.4,2.4)


Find the maximum and minimum values of z.

z = 5x + 8y

z = 5*2 + 8*0 = 10, minimum value of z

z = 5*4 + 8*0 = 20

z = 5*0 + 8*2 = 16

z = 5*0 + 8*4 = 32, maximum value of z

z = 5*2.4 + 8*2.4 = 31.2


Maximum value of z is: 32; when x = 0 and y = 4
Minimum value of z is: 10; when x = 2 and y = 0



Thanks for writing.


Staff
www.solving-math-problems.com


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